The next-to-leading-order QCD correction to inclusive J/ψ(Υ) production in Z^0 decay

Abstract

In this paper, we study the $J/\psi ({\rm Y})$ production in Z boson decay in color-singlet model(CSM). We calculate the next-to-leading-order (NLO) QCD correction to $Z\to Quarkonium+Q\bar{Q}$, the dominant contribution in the CSM, with the vector and axial-vector parts in $ZQ\bar{Q}$ vertex being treated separately. The results show that the vector and axial-vector parts have the same K factor (the ratio of NLO result to leading-order result) 1.13 with the renormalization scale $\mu$=2$m_c$ and $m_c=1.5GeV$, and the K factor falls to 0.918 when applying the Brodsky, Lepage, and Mackenzie(BLM) renormalization scale scheme with obtained ${\mu }_{BLM}=2.28GeV$ and $m_c=1.5$GeV. By including the contributions from the next-dominant ones, the photon and gluon fragmentation processes, the branching ratio for $Z\to J/{\psi }_{prompt}+X$ is $(7.3\sim 10.0)\times 10^{-5}$ with the uncertainty consideration for the renormalization scale and Charm quark mass. The results are about half of the central value of the experimental measurement 2.1$\times 10^{-4}$. Furthermore, the $J/\psi$ energy distribution in our calculation is not well consistent with the experimental data. Therefore, even at QCD NLO, the contribution to $Z\to J/{\psi }_{prompt}+X$ from the CSM can not fully account for the experimental measurement. And there should be contributions from other mechanisms, such as the color-octet(COM) contributions. We define $R_{c\bar{c}}=\frac{\Gamma (Z\to J/\psi c\bar{c}X)}{\Gamma (Z\to J/\psi X)}$ and obtain $R_{cc}=0.84$ for only CSM contribution and $R_{cc}=0.49$ for COM and CSM contributions together. Then $R_{cc}$ measurement could be used to clarify the COM contributions.

8 pages, 8 figures

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• QCD corrections to Upsilon production via color-octet states at the Tevatron and LHC
• The NLO fragmentation functions of heavy quarks into heavy quarkonia
• ${\chi }_{cJ}$ production associated with a $c\bar{c}$ pair at hadron colliders
• Next-to-leading order QCD corrections for the charmonium production via the channel $e^{+}{e}^{-}\to H(|c\bar{c}⟩)+\gamma$ round the $Z^0$ peak
• Observation of the Z $\to \psi {\ell }^{+}{\ell }^{-}$ decay in pp collisions at $\sqrt{s}=$ 13 TeV
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• Bottomonium production associated with a photon at a high luminosity $e^{+}{e}^{-}$ collider with next-to-leading order QCD corrections
• Comprehensive studies of ${\rm Y}$ inclusive production in $Z$ boson decay
• The studies on $Z\to {\rm Y}(1S)+g+g$ at the next-to-leading-order QCD accuracy
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• Impact of $Z\to {\eta }_{c,b}+g+g$ on the inclusive ${\eta }_{c,b}$ meson yield in $Z$-boson decay
• Next-to-leading order QCD corrections to $Z\to {\eta }_Q+Q+\bar{Q}$
• NLO QCD Corrections to Inclusive Charmonium and $B_c$ Meson Production in $W^{+}$ Decays
• The QED contribution to $J/\psi$ plus light hadrons production at B-factories